DLMF:8.21.E26 (Q3446)

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DLMF:8.21.E26
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    Statements

    DLMF defining formula
    f ⁢ ( a , z ) ∼ z a - 1 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ ( 1 - a ) 2 ⁢ k z 2 ⁢ k , asymptotic-expansion 𝑓 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript subscript 𝑘 0 superscript 1 𝑘 Pochhammer 1 𝑎 2 𝑘 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle f(a,z)\sim z^{a-1}\sum_{k=0}^{\infty}\frac{(-1)^{% k}{\left(1-a\right)_{2k}}}{z^{2k}},}}
    0 references
    Symbols used
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
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    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1vdec
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    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1wdec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1ddec
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    auxiliary function (locally)
    DLMF defining formula
    f ⁢ ( a , z ) 𝑓 𝑎 𝑧 {\displaystyle{\displaystyle f(a,z)}}
    xml-id
    C8.S21.XMD1.m1edec
    0 references

    Identifiers

     
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